{"group":{"group":{"id":2743,"name":"Satellite and Space Engineering Problems","lockable":false,"created_at":"2020-05-04T12:03:28.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"This is a series of problems looking at topics in satellite and space communications and systems engineering.\nMain topics covered will be communications link engineering and some (basic) orbital mechanics.","is_default":false,"created_by":437780,"badge_id":62,"featured":false,"trending":false,"solution_count_in_trending_period":102,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":2785,"published":true,"community_created":true,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is a series of problems looking at topics in satellite and space communications and systems engineering.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMain topics covered will be communications link engineering and some (basic) orbital mechanics.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 93px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 289.5px 46.5px; transform-origin: 289.5px 46.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 266.5px 21px; text-align: left; transform-origin: 266.5px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 259.067px 7.75px; transform-origin: 259.067px 7.75px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis is a series of problems looking at topics in satellite and space communications and systems engineering.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 266.5px 21px; text-align: left; transform-origin: 266.5px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 265.708px 7.75px; transform-origin: 265.708px 7.75px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMain topics covered will be communications link engineering and some (basic) orbital mechanics.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","published_at":"2022-01-04T17:42:12.000Z"},"current_player":null},"problems":[{"id":45492,"title":"SatCom #1: Wavelength of an electomagnetic wave","description":"*Satellite and Space Engineering - Problem #1*\r\n\r\n_This is the first of a series of problems looking at topics in satellite and space communications and systems engineering._\r\n\r\nAn easy one to start. You are given the frequency of an electromagnetic (RF) wave (in Hz). Calculate the wavelength (in m).\r\n\r\nYou should take the speed of light to be 299,792,458 m/s.\r\n\r\nThe input frequency must be a positive, real number.\r\n\r\nHint: See \u003chttps://pediaa.com/relationship-between-wavelength-and-frequency/\u003e\r\n\r\nExample: If the frequency is 500 MHz, wavelength is 0.599584916 m.\r\n\r\n_Some future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!_","description_html":"\u003cp\u003e\u003cb\u003eSatellite and Space Engineering - Problem #1\u003c/b\u003e\u003c/p\u003e\u003cp\u003e\u003ci\u003eThis is the first of a series of problems looking at topics in satellite and space communications and systems engineering.\u003c/i\u003e\u003c/p\u003e\u003cp\u003eAn easy one to start. You are given the frequency of an electromagnetic (RF) wave (in Hz). Calculate the wavelength (in m).\u003c/p\u003e\u003cp\u003eYou should take the speed of light to be 299,792,458 m/s.\u003c/p\u003e\u003cp\u003eThe input frequency must be a positive, real number.\u003c/p\u003e\u003cp\u003eHint: See \u003ca href = \"https://pediaa.com/relationship-between-wavelength-and-frequency/\"\u003ehttps://pediaa.com/relationship-between-wavelength-and-frequency/\u003c/a\u003e\u003c/p\u003e\u003cp\u003eExample: If the frequency is 500 MHz, wavelength is 0.599584916 m.\u003c/p\u003e\u003cp\u003e\u003ci\u003eSome future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!\u003c/i\u003e\u003c/p\u003e","function_template":"function l = freq2wave(f)\r\n  l = f;\r\nend","test_suite":"%%\r\nf = 500e6;\r\ny_correct = 0.599584916;\r\nassert(isequal(freq2wave(f),y_correct))\r\n\r\n%%\r\nf = 200;\r\ny_correct = 1.498962290000000e+06;\r\nassert(isequal(freq2wave(f),y_correct))\r\n\r\n%%\r\ns=importdata('freq2wave.m');\r\ny_correct=false;\r\nassert(isequal(sum(contains(s,'regexp')),y_correct))\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":0,"created_by":437780,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":256,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-05-04T11:11:26.000Z","updated_at":"2026-04-01T13:48:51.000Z","published_at":"2020-05-04T11:35:20.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSatellite and Space Engineering - Problem #1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eThis is the first of a series of problems looking at topics in satellite and space communications and systems engineering.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn easy one to start. You are given the frequency of an electromagnetic (RF) wave (in Hz). Calculate the wavelength (in m).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou should take the speed of light to be 299,792,458 m/s.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe input frequency must be a positive, real number.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: See\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://pediaa.com/relationship-between-wavelength-and-frequency/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://pediaa.com/relationship-between-wavelength-and-frequency/\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample: If the frequency is 500 MHz, wavelength is 0.599584916 m.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSome future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45493,"title":"SatCom #2: Gain of a circular 'dish' antenna","description":"Satellite and Space Engineering - Problem #2\r\nThis is part of a series of problems looking at topics in satellite and space communications and systems engineering.\r\nDetermine the gain (in dBi) of a circular 'dish' antenna.\r\nYou are given the diameter of the antenna (in m), the frequency of operation (in Hz) and the antenna efficiency (as a %). Calculate the gain of the antenna (in dBi).\r\nYou should take the speed of light to be 299,792,458 m/s.\r\nHint: See \u003chttps://en.wikipedia.org/wiki/Parabolic_antenna#Gain\u003e - but don't forget to convert to dBi!\r\nExample: The gain of a typical direct-to-home 60cm TV receiving antenna at 12 GHz is around 36 dBi.\r\nSome future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 273px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 136.5px; transform-origin: 407px 136.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 157.5px 8px; transform-origin: 157.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSatellite and Space Engineering - Problem #2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 366.5px 8px; transform-origin: 366.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eThis is part of a series of problems looking at topics in satellite and space communications and systems engineering.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 171.5px 8px; transform-origin: 171.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDetermine the gain (in dBi) of a circular 'dish' antenna.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 380.5px 8px; transform-origin: 380.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou are given the diameter of the antenna (in m), the frequency of operation (in Hz) and the antenna efficiency (as a %). Calculate the gain of the antenna (in dBi).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 182px 8px; transform-origin: 182px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou should take the speed of light to be 299,792,458 m/s.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.5px 8px; transform-origin: 28.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint: See\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Parabolic_antenna#Gain\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e\u0026lt;https://en.wikipedia.org/wiki/Parabolic_antenna#Gain\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.5px 8px; transform-origin: 114.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u0026gt; - but don't forget to convert to dBi!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 319.5px 8px; transform-origin: 319.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample: The gain of a typical direct-to-home 60cm TV receiving antenna at 12 GHz is around 36 dBi.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eSome future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function gain = ant_gain(diam,freq,eff)\r\n  gain = diam+freq+eff;\r\nend","test_suite":"%%\r\nd = 10;\r\nf = 299792458/pi;\r\ne = 100;\r\ny_correct = 20;\r\nassert(abs(ant_gain(d,f,e)-y_correct)\u003c1e-8)\r\n\r\n%%\r\nd = 0.6;\r\nf = 12e9;\r\ne = 70;\r\ny_correct = 36.004213724092068;\r\nassert(abs(ant_gain(d,f,e)-y_correct)\u003c1e-8)\r\n\r\n%%\r\nd = 30;\r\nf = 6e9;\r\ne = 65;\r\ny_correct = 63.641167063818799;\r\nassert(abs(ant_gain(d,f,e)-y_correct)\u003c1e-8)\r\n\r\n%%\r\ns=importdata('ant_gain.m');\r\ny_correct=false;\r\nassert(isequal(sum(contains(s,'regexp')),y_correct))\r\n","published":true,"deleted":false,"likes_count":6,"comments_count":3,"created_by":437780,"edited_by":223089,"edited_at":"2022-05-20T19:19:27.000Z","deleted_by":null,"deleted_at":null,"solvers_count":197,"test_suite_updated_at":"2022-05-20T19:19:27.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-05-04T11:40:46.000Z","updated_at":"2026-04-01T14:08:07.000Z","published_at":"2020-05-04T12:00:04.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSatellite and Space Engineering - Problem #2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eThis is part of a series of problems looking at topics in satellite and space communications and systems engineering.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDetermine the gain (in dBi) of a circular 'dish' antenna.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are given the diameter of the antenna (in m), the frequency of operation (in Hz) and the antenna efficiency (as a %). Calculate the gain of the antenna (in dBi).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou should take the speed of light to be 299,792,458 m/s.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: See\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Parabolic_antenna#Gain\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://en.wikipedia.org/wiki/Parabolic_antenna#Gain\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt; - but don't forget to convert to dBi!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample: The gain of a typical direct-to-home 60cm TV receiving antenna at 12 GHz is around 36 dBi.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSome future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":45494,"title":"SatCom #3: Free Space Path Loss","description":"*Satellite and Space Engineering - Problem #3*\r\n\r\n_This is part of a series of problems looking at topics in satellite and space communications and systems engineering._\r\n\r\nDetermine the \"Free Space Path Loss\" (dB) between a transmit and receive antenna. (Note that \"Free Space Path Loss\" is *not* the same as \"Spreading Loss\" (inverse-square loss), as it is defined as the loss between the input port of a transmitting isotropic antenna and the output port of a receiving isotropic antenna. As it contains (hidden inside the formula) also the formulas for the transmitting and receiving isotropic antenna gains, \"Free Space Path Loss\" has, perhaps surprisingly at first thought, a frequency-dependent term).\r\n\r\nYou are given the distance between the transmitting and receiving antennas in a satellite link (in m) and the frequency of operation (in Hz). Calculate the \"Free Space Loss\" (in dB).\r\n\r\nYou should take the speed of light to be 299,792,458 m/s.\r\n\r\nHint: See \u003chttps://en.wikipedia.org/wiki/Free-space_path_loss#Free-space_path_loss_formula\u003e - but don't forget to convert to dB!\r\n\r\nExample: The Free Space Path Loss from an antenna on the ground to a Geostationary satellite directly overhead (roughly 35,786 km altitude) at 10 GHz is around 203.5 dB.\r\n\r\n_Some future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!_","description_html":"\u003cp\u003e\u003cb\u003eSatellite and Space Engineering - Problem #3\u003c/b\u003e\u003c/p\u003e\u003cp\u003e\u003ci\u003eThis is part of a series of problems looking at topics in satellite and space communications and systems engineering.\u003c/i\u003e\u003c/p\u003e\u003cp\u003eDetermine the \"Free Space Path Loss\" (dB) between a transmit and receive antenna. (Note that \"Free Space Path Loss\" is \u003cb\u003enot\u003c/b\u003e the same as \"Spreading Loss\" (inverse-square loss), as it is defined as the loss between the input port of a transmitting isotropic antenna and the output port of a receiving isotropic antenna. As it contains (hidden inside the formula) also the formulas for the transmitting and receiving isotropic antenna gains, \"Free Space Path Loss\" has, perhaps surprisingly at first thought, a frequency-dependent term).\u003c/p\u003e\u003cp\u003eYou are given the distance between the transmitting and receiving antennas in a satellite link (in m) and the frequency of operation (in Hz). Calculate the \"Free Space Loss\" (in dB).\u003c/p\u003e\u003cp\u003eYou should take the speed of light to be 299,792,458 m/s.\u003c/p\u003e\u003cp\u003eHint: See \u003ca href = \"https://en.wikipedia.org/wiki/Free-space_path_loss#Free-space_path_loss_formula\"\u003ehttps://en.wikipedia.org/wiki/Free-space_path_loss#Free-space_path_loss_formula\u003c/a\u003e - but don't forget to convert to dB!\u003c/p\u003e\u003cp\u003eExample: The Free Space Path Loss from an antenna on the ground to a Geostationary satellite directly overhead (roughly 35,786 km altitude) at 10 GHz is around 203.5 dB.\u003c/p\u003e\u003cp\u003e\u003ci\u003eSome future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!\u003c/i\u003e\u003c/p\u003e","function_template":"function loss = FSPL(dist,freq)\r\n  loss = dist+freq;\r\nend","test_suite":"%%\r\nd = 35786000;\r\nf = 10e9;\r\ny_correct = 2.035220463738069e+02;\r\nassert(abs(FSPL(d,f)-y_correct)\u003c10*eps(y_correct))\r\n\r\n%%\r\nd = 41950000;\r\nf = 1.98e9;\r\ny_correct = 1.908357263304084e+02;\r\nassert(abs(FSPL(d,f)-y_correct)\u003c10*eps(y_correct))\r\n\r\n%%\r\ns=importdata('FSPL.m');\r\ny_correct=false;\r\nassert(isequal(sum(contains(s,'regexp')),y_correct))\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":437780,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":132,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-05-04T17:11:35.000Z","updated_at":"2026-04-01T14:20:22.000Z","published_at":"2020-05-04T17:15:31.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSatellite and Space Engineering - Problem #3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eThis is part of a series of problems looking at topics in satellite and space communications and systems engineering.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDetermine the \\\"Free Space Path Loss\\\" (dB) between a transmit and receive antenna. (Note that \\\"Free Space Path Loss\\\" is\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enot\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the same as \\\"Spreading Loss\\\" (inverse-square loss), as it is defined as the loss between the input port of a transmitting isotropic antenna and the output port of a receiving isotropic antenna. As it contains (hidden inside the formula) also the formulas for the transmitting and receiving isotropic antenna gains, \\\"Free Space Path Loss\\\" has, perhaps surprisingly at first thought, a frequency-dependent term).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are given the distance between the transmitting and receiving antennas in a satellite link (in m) and the frequency of operation (in Hz). Calculate the \\\"Free Space Loss\\\" (in dB).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou should take the speed of light to be 299,792,458 m/s.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: See\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Free-space_path_loss#Free-space_path_loss_formula\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://en.wikipedia.org/wiki/Free-space_path_loss#Free-space_path_loss_formula\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt; - but don't forget to convert to dB!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample: The Free Space Path Loss from an antenna on the ground to a Geostationary satellite directly overhead (roughly 35,786 km altitude) at 10 GHz is around 203.5 dB.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSome future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45553,"title":"SatCom #4: Satellite Orbit Altitude","description":"Satellite and Space Engineering - Problem #4\r\nThis is part of a series of problems looking at topics in satellite and space communications and systems engineering.\r\nDetermine the altitude (height above the surface of the Earth) for a satellite in a circular Earth orbit with a known orbit period.\r\nYou are given the satellite orbit period (in s). Calculate the orbit altitude (in km).\r\nYou should take the radius of the Earth to be 6371km, the mass of the Earth to be 5.9722e24 kg and Newton's Universal Gravitational Constant to be 6.6743015e-11 m3/kg/s.\r\nHints: 1) Newton's Law of Universal Gravitation will tell you the force between the satellite and the Earth (see: \u003chttps://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation\u003e); 2) The centripetal force maintaining the orbit (see: \u003chttps://en.wikipedia.org/wiki/Centripetal_force#Formula\u003e) should be equal to the gravitational force; 3) Hmmm... but what about the mass of the satellite?\r\nExample: The altitude of a geostationary satellite, with orbit period 86164.0905 s is around 35,793 km.\r\nSome future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 357px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 178.5px; transform-origin: 407px 178.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 157.5px 8px; transform-origin: 157.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSatellite and Space Engineering - Problem #4\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 366.5px 8px; transform-origin: 366.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eThis is part of a series of problems looking at topics in satellite and space communications and systems engineering.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 370px 8px; transform-origin: 370px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDetermine the altitude (height above the surface of the Earth) for a satellite in a circular Earth orbit with a known orbit period.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 249.5px 8px; transform-origin: 249.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou are given the satellite orbit period (in s). Calculate the orbit altitude (in km).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 380px 8px; transform-origin: 380px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou should take the radius of the Earth to be 6371km, the mass of the Earth to be 5.9722e24 kg and Newton's Universal Gravitational Constant to be 6.6743015e-11 m3/kg/s.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 341px 8px; transform-origin: 341px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHints: 1) Newton's Law of Universal Gravitation will tell you the force between the satellite and the Earth (see:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"perspective-origin: 225.5px 8px; transform-origin: 225.5px 8px; \"\u003e\u0026lt;https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 152.5px 8px; transform-origin: 152.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u0026gt;); 2) The centripetal force maintaining the orbit (see:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Centripetal_force#Formula\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e\u0026lt;https://en.wikipedia.org/wiki/Centripetal_force#Formula\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 190px 8px; transform-origin: 190px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u0026gt;) should be equal to the gravitational force; 3) Hmmm... but what about the mass of the satellite?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 321px 8px; transform-origin: 321px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample: The altitude of a geostationary satellite, with orbit period 86164.0905 s is around 35,793 km.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eSome future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function alt = OrbitAltitude(Period)\r\n%Determine the orbit altitude (km) for a circular orbit of period 'Period' (s)\r\n  alt = 0;\r\nend","test_suite":"%%\r\nfiletext = fileread('OrbitAltitude.m');\r\nassert(isempty(strfind(filetext, 'regexp')))\r\n\r\n%%\r\np = 86164.0905;\r\ny_correct = 35793;\r\nOrbitAltitude(p)-y_correct\r\nassert(abs(OrbitAltitude(p)-y_correct)\u003c0.5)\r\n\r\n%%\r\np = 92.5*60;\r\ny_correct = 404.2002;\r\nOrbitAltitude(p)-y_correct\r\nassert(abs(OrbitAltitude(p)-y_correct)\u003c0.05)\r\n\r\n%%\r\np = 34123;\r\ny_correct = 16367;\r\nOrbitAltitude(p)-y_correct\r\nassert(abs(OrbitAltitude(p)-y_correct)\u003c0.5)\r\n","published":true,"deleted":false,"likes_count":9,"comments_count":5,"created_by":437780,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":180,"test_suite_updated_at":"2022-02-27T14:25:58.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-05-21T08:30:34.000Z","updated_at":"2026-04-01T15:28:16.000Z","published_at":"2020-05-21T08:38:54.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSatellite and Space Engineering - Problem #4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eThis is part of a series of problems looking at topics in satellite and space communications and systems engineering.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDetermine the altitude (height above the surface of the Earth) for a satellite in a circular Earth orbit with a known orbit period.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are given the satellite orbit period (in s). Calculate the orbit altitude (in km).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou should take the radius of the Earth to be 6371km, the mass of the Earth to be 5.9722e24 kg and Newton's Universal Gravitational Constant to be 6.6743015e-11 m3/kg/s.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHints: 1) Newton's Law of Universal Gravitation will tell you the force between the satellite and the Earth (see:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;); 2) The centripetal force maintaining the orbit (see:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Centripetal_force#Formula\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://en.wikipedia.org/wiki/Centripetal_force#Formula\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;) should be equal to the gravitational force; 3) Hmmm... but what about the mass of the satellite?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample: The altitude of a geostationary satellite, with orbit period 86164.0905 s is around 35,793 km.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSome future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":45797,"title":"SatCom #5: Determine Elliptical Orbit Parameters","description":"*Satellite and Space Engineering - Problem #5*\r\n\r\n_This is part of a series of problems looking at topics in satellite and space communications and systems engineering._\r\n\r\nMany satellites orbit the Earth along an elliptical path, where the Earth is centred at one of the focii of the ellipse. Typically we might know the apogee (maximum distance of the satellite from the Earth's surface) and perigee (smallest distance from the Earth) of the satellite orbit. In order to model the orbit, however, we often need to know the parameters of the orbit ellipse, i.e. the semi-major axis (half the maximum dimension of the ellipse), the semi-minor axis (half of the minimum dimension) and the eccentricity (a measure of how circular the orbit is).\r\n\r\nYou are given the apogee altitude (in km) and the perigee altitude (in km). Calculate the semi-major axis length (in km), the semi-minor axis length (in km) and the eccentricity (as a ratio).\r\n\r\nYou should take the radius of the Earth to be 6371km.\r\n\r\nHint: See: \u003chttps://www.physicsforums.com/threads/eccentricity-of-orbit-apogee-and-perigee-positions-and-distances.248164/\u003e .\r\n\r\nExample 1: Assume that the International Space Station is in an orbit with (roughly) an apogee of 381 km and a perigee of 372 km. It therefore has a semi-major axis of 6,747.5 km, a semi-minor axis of 6,747.498 km and an eccentricity of 0.000669 (i.e. its orbit is virtually circular).\r\n\r\nExample 2: A 'Molnya' orbit is a highly-eliptical inclined orbit with good coverage over high and low latitudes. It has (roughly) an apogee of 39,700 km and a perigee of 600 km. It has a semi-major axis of around 26,500 km, a semi-minor axis of around 17,900 km and an eccentricity of 0.737.\r\n\r\n_Some future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!_","description_html":"\u003cp\u003e\u003cb\u003eSatellite and Space Engineering - Problem #5\u003c/b\u003e\u003c/p\u003e\u003cp\u003e\u003ci\u003eThis is part of a series of problems looking at topics in satellite and space communications and systems engineering.\u003c/i\u003e\u003c/p\u003e\u003cp\u003eMany satellites orbit the Earth along an elliptical path, where the Earth is centred at one of the focii of the ellipse. Typically we might know the apogee (maximum distance of the satellite from the Earth's surface) and perigee (smallest distance from the Earth) of the satellite orbit. In order to model the orbit, however, we often need to know the parameters of the orbit ellipse, i.e. the semi-major axis (half the maximum dimension of the ellipse), the semi-minor axis (half of the minimum dimension) and the eccentricity (a measure of how circular the orbit is).\u003c/p\u003e\u003cp\u003eYou are given the apogee altitude (in km) and the perigee altitude (in km). Calculate the semi-major axis length (in km), the semi-minor axis length (in km) and the eccentricity (as a ratio).\u003c/p\u003e\u003cp\u003eYou should take the radius of the Earth to be 6371km.\u003c/p\u003e\u003cp\u003eHint: See: \u003ca href = \"https://www.physicsforums.com/threads/eccentricity-of-orbit-apogee-and-perigee-positions-and-distances.248164/\"\u003ehttps://www.physicsforums.com/threads/eccentricity-of-orbit-apogee-and-perigee-positions-and-distances.248164/\u003c/a\u003e .\u003c/p\u003e\u003cp\u003eExample 1: Assume that the International Space Station is in an orbit with (roughly) an apogee of 381 km and a perigee of 372 km. It therefore has a semi-major axis of 6,747.5 km, a semi-minor axis of 6,747.498 km and an eccentricity of 0.000669 (i.e. its orbit is virtually circular).\u003c/p\u003e\u003cp\u003eExample 2: A 'Molnya' orbit is a highly-eliptical inclined orbit with good coverage over high and low latitudes. It has (roughly) an apogee of 39,700 km and a perigee of 600 km. It has a semi-major axis of around 26,500 km, a semi-minor axis of around 17,900 km and an eccentricity of 0.737.\u003c/p\u003e\u003cp\u003e\u003ci\u003eSome future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!\u003c/i\u003e\u003c/p\u003e","function_template":"function [semi_major, semi_minor, ecc] = orbit_ellipse(apogee, perigee)\r\n  semi_major = 1;\r\n  semi_minor = 1;\r\n  ecc = 0;\r\nend","test_suite":"%%\r\n%International Space Station\r\napogee = 381;\r\nperigee = 372;\r\ny_correct = [6747.5 6747.498499444 6.669136717302705e-04];\r\n[semimaj, semimin, ecc] = orbit_ellipse(apogee, perigee)\r\nassert(abs(semimaj-y_correct(1))\u003c0.000001,'Semi-major axis wrong')\r\nassert(abs(semimin-y_correct(2))\u003c0.000001,'Semi-minor axis wrong')\r\nassert(abs(ecc-y_correct(3))\u003c0.000001,'Eccentricity wrong')\r\n\r\n%%\r\n%Molnya Orbit\r\napogee = 39700;\r\nperigee = 600;\r\ny_correct = [26521 1.792096372966588e+04 0.737151691112703];\r\n[semimaj, semimin, ecc] = orbit_ellipse(apogee, perigee)\r\nassert(abs(semimaj-y_correct(1))\u003c0.000001,'Semi-major axis wrong')\r\nassert(abs(semimin-y_correct(2))\u003c0.000001,'Semi-minor axis wrong')\r\nassert(abs(ecc-y_correct(3))\u003c0.000001,'Eccentricity wrong')\r\n\r\n%%\r\n%Orbit of the Moon around the Earth\r\napogee = 405400;\r\nperigee = 362600;\r\ny_correct = [390371 3.897839884359028e+05 0.054819645926567];\r\n[semimaj, semimin, ecc] = orbit_ellipse(apogee, perigee)\r\nassert(abs(semimaj-y_correct(1))\u003c0.000001,'Semi-major axis wrong')\r\nassert(abs(semimin-y_correct(2))\u003c0.000001,'Semi-minor axis wrong')\r\nassert(abs(ecc-y_correct(3))\u003c0.000001,'Eccentricity wrong')\r\n\r\n%%\r\n%Circular Geostationary Orbit\r\napogee = 35793;\r\nperigee = 35793;\r\ny_correct = [42164 42164 0];\r\n[semimaj, semimin, ecc] = orbit_ellipse(apogee, perigee)\r\nassert(abs(semimaj-y_correct(1))\u003c0.000001,'Semi-major axis wrong')\r\nassert(abs(semimin-y_correct(2))\u003c0.000001,'Semi-minor axis wrong')\r\nassert(abs(ecc-y_correct(3))\u003c0.000001,'Eccentricity wrong')\r\n\r\n%%\r\ns=importdata('orbit_ellipse.m');\r\ny_correct=false;\r\nassert(isequal(sum(contains(s,'regexp')),y_correct))\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":4,"created_by":437780,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":96,"test_suite_updated_at":"2020-06-10T15:35:14.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-06-08T11:01:37.000Z","updated_at":"2026-03-27T17:35:15.000Z","published_at":"2020-06-10T15:35:14.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSatellite and Space Engineering - Problem #5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eThis is part of a series of problems looking at topics in satellite and space communications and systems engineering.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMany satellites orbit the Earth along an elliptical path, where the Earth is centred at one of the focii of the ellipse. Typically we might know the apogee (maximum distance of the satellite from the Earth's surface) and perigee (smallest distance from the Earth) of the satellite orbit. In order to model the orbit, however, we often need to know the parameters of the orbit ellipse, i.e. the semi-major axis (half the maximum dimension of the ellipse), the semi-minor axis (half of the minimum dimension) and the eccentricity (a measure of how circular the orbit is).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are given the apogee altitude (in km) and the perigee altitude (in km). Calculate the semi-major axis length (in km), the semi-minor axis length (in km) and the eccentricity (as a ratio).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou should take the radius of the Earth to be 6371km.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: See:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.physicsforums.com/threads/eccentricity-of-orbit-apogee-and-perigee-positions-and-distances.248164/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://www.physicsforums.com/threads/eccentricity-of-orbit-apogee-and-perigee-positions-and-distances.248164/\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt; .\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 1: Assume that the International Space Station is in an orbit with (roughly) an apogee of 381 km and a perigee of 372 km. It therefore has a semi-major axis of 6,747.5 km, a semi-minor axis of 6,747.498 km and an eccentricity of 0.000669 (i.e. its orbit is virtually circular).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 2: A 'Molnya' orbit is a highly-eliptical inclined orbit with good coverage over high and low latitudes. It has (roughly) an apogee of 39,700 km and a perigee of 600 km. It has a semi-major axis of around 26,500 km, a semi-minor axis of around 17,900 km and an eccentricity of 0.737.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSome future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45800,"title":"SatCom #6: Inclination of a Sun-Synchronous Orbit","description":"Satellite and Space Engineering - Problem #5\r\nThis is part of a series of problems looking at topics in satellite and space communications and systems engineering.\r\nA particularly interesting (and useful) orbit is the 'Sun-Synchronous Orbit.' This orbit has the special feature that the plane of the orbit precesses (rotates) in inertial space at exactly the same rate as the earth rotates around the sun. Therefore, the orbit plane always maintains a fixed angle with respect to the sun, which means that the satellite always passes over the same point on the ground at the same local mean solar time. Now, satellite orbits, in the absence of external forces, will not precess, but will remain on a plane fixed with respect to inertial space. However, the unequal forces on the satellite caused by the equatorial bulge of the Earth tends to make inclined orbits precess, and by tuning the orbit inclination and altitude (actually the semi-major axis and eccentricity of the orbit ellipse), the orbit can be made to precess at just the right angular rate to maintain a fixed direction towards the sun. (See: \u003chttps://en.wikipedia.org/wiki/Sun-synchronous_orbit\u003e for more information about such orbits.)\r\nYou are given the satellite orbit's apogee and perigee altitudes (in km). Calculate the inclination needed to achieve a sun-synchronous orbit.\r\nYou should take the radius of the Earth to be 6371km.\r\nHint : If you are not sure about how to derive the semi-major axis and eccentricity of the orbit given its apogee altitude, perigee altitude and the Earth's radius, you probably ought to try Problem 45797. SatCom #5: Determine Elliptical Orbit Parameters first ( \u003chttps://www.mathworks.com/matlabcentral/cody/problems/45797-satcom-5-determine-elliptical-orbit-parameters\u003e ).\r\nExample: The CLOUDSAT satellite has an apogee of 710 km and a perigee of 709 km. It's orbit inclination is approximately 98.2 degrees.\r\nSome future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 525px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 262.5px; transform-origin: 407px 262.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 157.5px 8px; transform-origin: 157.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSatellite and Space Engineering - Problem #5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 366.5px 8px; transform-origin: 366.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eThis is part of a series of problems looking at topics in satellite and space communications and systems engineering.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 189px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 94.5px; text-align: left; transform-origin: 384px 94.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA particularly interesting (and useful) orbit is the 'Sun-Synchronous Orbit.' This orbit has the special feature that the plane of the orbit precesses (rotates) in inertial space at exactly the same rate as the earth rotates around the sun. Therefore, the orbit plane always maintains a fixed angle with respect to the sun, which means that the satellite always passes over the same point on the ground at the same local mean solar time. Now, satellite orbits, in the absence of external forces, will not precess, but will remain on a plane fixed with respect to inertial space. However, the unequal forces on the satellite caused by the equatorial bulge of the Earth tends to make inclined orbits precess, and by tuning the orbit inclination and altitude (actually the semi-major axis and eccentricity of the orbit ellipse), the orbit can be made to precess at just the right angular rate to maintain a fixed direction towards the sun. (See:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Sun-synchronous_orbit\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e\u0026lt;https://en.wikipedia.org/wiki/Sun-synchronous_orbit\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16.5px 8px; transform-origin: 16.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u0026gt; for more information about such orbits.)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 382px 8px; transform-origin: 382px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou are given the satellite orbit's apogee and perigee altitudes (in km). Calculate the inclination needed to achieve a sun-synchronous orbit.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 170px 8px; transform-origin: 170px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou should take the radius of the Earth to be 6371km.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 372.5px 8px; transform-origin: 372.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint : If you are not sure about how to derive the semi-major axis and eccentricity of the orbit given its apogee altitude, perigee altitude and the Earth's radius, you probably ought to try\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 165.5px 8px; transform-origin: 165.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem 45797. SatCom #5: Determine Elliptical Orbit Parameters\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18px 8px; transform-origin: 18px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e first (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45797-satcom-5-determine-elliptical-orbit-parameters\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e\u0026lt;https://www.mathworks.com/matlabcentral/cody/problems/45797-satcom-5-determine-elliptical-orbit-parameters\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.5px 8px; transform-origin: 10.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u0026gt; ).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample: The CLOUDSAT satellite has an apogee of 710 km and a perigee of 709 km. It's orbit inclination is approximately 98.2 degrees.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eSome future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function incl=SSO_inclination(apogee, perigee)\r\n  incl = apogee+perigee;\r\nend","test_suite":"%%\r\napogee = 450;\r\nperigee = 450;\r\ny_correct = 97.188082537370235;\r\nincl = SSO_inclination(apogee, perigee)\r\nassert(abs(incl-y_correct)\u003c1e-10)\r\n\r\n%%\r\napogee = 282;\r\nperigee = 282;\r\ny_correct = 96.584499153516305;\r\nincl = SSO_inclination(apogee, perigee)\r\nassert(abs(incl-y_correct)\u003c1e-10)\r\n\r\n%%\r\napogee = 5172;\r\nperigee = 5172;\r\ny_correct = 1.420787507850000e+02;\r\nincl = SSO_inclination(apogee, perigee)\r\nassert(abs(incl-y_correct)\u003c1e-10)\r\n\r\n%%\r\napogee = 9344;\r\nperigee = 1000;\r\ny_correct = 1.265994678603832e+02;\r\nincl = SSO_inclination(apogee, perigee)\r\nassert(abs(incl-y_correct)\u003c1e-10)\r\n\r\n%%\r\n%Cloudsat\r\napogee = 710;\r\nperigee = 709;\r\ny_correct = 98.198070972920874;\r\nincl = SSO_inclination(apogee, perigee)\r\nassert(abs(incl-y_correct)\u003c1e-10)\r\n\r\n%%\r\ns=importdata('SSO_inclination.m');\r\ny_correct=false;\r\nassert(isequal(sum(contains(s,'regexp')),y_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":3,"created_by":437780,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":68,"test_suite_updated_at":"2021-08-31T08:00:36.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-06-08T11:16:10.000Z","updated_at":"2026-04-02T18:41:58.000Z","published_at":"2020-06-11T21:22:58.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSatellite and Space Engineering - Problem #5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eThis is part of a series of problems looking at topics in satellite and space communications and systems engineering.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA particularly interesting (and useful) orbit is the 'Sun-Synchronous Orbit.' This orbit has the special feature that the plane of the orbit precesses (rotates) in inertial space at exactly the same rate as the earth rotates around the sun. Therefore, the orbit plane always maintains a fixed angle with respect to the sun, which means that the satellite always passes over the same point on the ground at the same local mean solar time. Now, satellite orbits, in the absence of external forces, will not precess, but will remain on a plane fixed with respect to inertial space. However, the unequal forces on the satellite caused by the equatorial bulge of the Earth tends to make inclined orbits precess, and by tuning the orbit inclination and altitude (actually the semi-major axis and eccentricity of the orbit ellipse), the orbit can be made to precess at just the right angular rate to maintain a fixed direction towards the sun. (See:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Sun-synchronous_orbit\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://en.wikipedia.org/wiki/Sun-synchronous_orbit\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt; for more information about such orbits.)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are given the satellite orbit's apogee and perigee altitudes (in km). Calculate the inclination needed to achieve a sun-synchronous orbit.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou should take the radius of the Earth to be 6371km.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint : If you are not sure about how to derive the semi-major axis and eccentricity of the orbit given its apogee altitude, perigee altitude and the Earth's radius, you probably ought to try\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem 45797. SatCom #5: Determine Elliptical Orbit Parameters\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e first (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45797-satcom-5-determine-elliptical-orbit-parameters\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://www.mathworks.com/matlabcentral/cody/problems/45797-satcom-5-determine-elliptical-orbit-parameters\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt; ).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample: The CLOUDSAT satellite has an apogee of 710 km and a perigee of 709 km. It's orbit inclination is approximately 98.2 degrees.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSome future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":45803,"title":"SatCom #7: Thermal Noise in a Receiver ","description":"Satellite and Space Engineering - Problem #7\r\nThis is part of a series of problems looking at topics in satellite and space communications and systems engineering.\r\nDetermine the thermal (Gaussian) noise power (dBW) in a radio receiver (in this case we are thinking of a satellite receiver, but the approach is generic to all radio receivers).\r\nYou are given the bandwidth of the receiver (in Hz) and the receiving system noise temperature (in Kelvin).\r\nYou should take Boltzmann's constant to be 1.380649×10^−23 J/K.\r\nHint: See https://en.wikipedia.org/wiki/Noise_figure#General - but don't forget to convert to dB!\r\nExample: The thermal noise power in a satellite receiver with a bandwidth of 2 MHz and a receiving system noise temperature of 200 K is around -142.6 dB.\r\nSome future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 294px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 147px; transform-origin: 407px 147px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 157.5px 8px; transform-origin: 157.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSatellite and Space Engineering - Problem #7\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 366.5px 8px; transform-origin: 366.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eThis is part of a series of problems looking at topics in satellite and space communications and systems engineering.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 359.5px 8px; transform-origin: 359.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDetermine the thermal (Gaussian) noise power (dBW) in a radio receiver (in this case we are thinking of a satellite receiver, but the approach is generic to all radio receivers).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 334.5px 8px; transform-origin: 334.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou are given the bandwidth of the receiver (in Hz) and the receiving system noise temperature (in Kelvin).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 209px 8px; transform-origin: 209px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou should take Boltzmann's constant to be 1.380649×10^−23 J/K.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.5px 8px; transform-origin: 28.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint: See\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Noise_figure#General\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ehttps://en.wikipedia.org/wiki/Noise_figure#General\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 109px 8px; transform-origin: 109px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e - but don't forget to convert to dB!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 354px 8px; transform-origin: 354px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample: The thermal noise power in a satellite receiver with a bandwidth of 2 MHz and a receiving system noise temperature of 200 K is around -142.6 dB.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eSome future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function power = thermal_noise_power(Bandwidth, Noise_Temp)\r\n  power = Bandwidth+Noise_Temp;\r\nend","test_suite":"%%\r\nBandwidth = 2e6;\r\nNoise_Temp = 200;\r\nN_Power=thermal_noise_power(Bandwidth, Noise_Temp)\r\ny_correct = -142.5786;\r\nassert(abs(N_Power-y_correct)\u003c0.001)\r\n\r\n%%\r\nBandwidth = 20e6;\r\nNoise_Temp = 120;\r\nN_Power=thermal_noise_power(Bandwidth, Noise_Temp)\r\ny_correct = -134.7971;\r\nassert(abs(N_Power-y_correct)\u003c0.001)\r\n\r\n%%\r\nBandwidth = 1;\r\nNoise_Temp = 290;\r\nN_Power=thermal_noise_power(Bandwidth, Noise_Temp)\r\ny_correct = -203.9752;\r\nassert(abs(N_Power-y_correct)\u003c0.001)\r\n\r\n%%\r\ns=fileread('thermal_noise_power.m');\r\ny_correct=false;\r\nassert(isequal(sum(contains(s,'regexp')),y_correct))\r\n","published":true,"deleted":false,"likes_count":6,"comments_count":3,"created_by":437780,"edited_by":223089,"edited_at":"2023-03-01T17:32:20.000Z","deleted_by":null,"deleted_at":null,"solvers_count":85,"test_suite_updated_at":"2023-03-01T17:32:20.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-06-09T20:05:50.000Z","updated_at":"2026-04-02T18:47:36.000Z","published_at":"2020-09-25T16:48:19.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSatellite and Space Engineering - Problem #7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eThis is part of a series of problems looking at topics in satellite and space communications and systems engineering.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDetermine the thermal (Gaussian) noise power (dBW) in a radio receiver (in this case we are thinking of a satellite receiver, but the approach is generic to all radio receivers).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are given the bandwidth of the receiver (in Hz) and the receiving system noise temperature (in Kelvin).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou should take Boltzmann's constant to be 1.380649×10^−23 J/K.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: See\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Noise_figure#General\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttps://en.wikipedia.org/wiki/Noise_figure#General\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e - but don't forget to convert to dB!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample: The thermal noise power in a satellite receiver with a bandwidth of 2 MHz and a receiving system noise temperature of 200 K is around -142.6 dB.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSome future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":45806,"title":"SatCom #8: Satellite Link Budget ","description":"Satellite and Space Engineering - Problem #8\r\nThis is part of a series of problems looking at topics in satellite and space communications and systems engineering.\r\nlf you have competed the previous exercises in this series, you will have more-or-less everything that you need to complete this problem.\r\nKnowing the parameters of a radio transmitter and receiver, determine the wanted signal power (dBW) in the radio receiver (in this case we are thinking of a satellite receiver, but the approach is generic to all radio receivers).\r\nYou are given power (dBW) of the signal applied to the transmitting dish antenna, the diameters (m) and efficiencies (%) of the transmitting and receiving dishes, the path length (km) between the transmitting and receiving antennas, and the frequency of the transmitted signal (GHz). \r\nHint: See https://en.wikipedia.org/wiki/Link_budget#Equation - For this simplified exercise, you should ignore transmitter, receiver and miscelaneous losses.\r\nExample: For a Ka-Band GSO space-to-Earth link at 17.7 GHz and of path length 41,130.13 km, where the satellite antenna has an input RF power of 9.5 dBW, a diameter of 75cm and an efficiency of 70%, and the signal is received on an Earth-station antenna of diameter 65cm and efficiency 65%, the RF power in the satellite receiver is around -119.1 dBW.\r\nSome future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 399px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 199.5px; transform-origin: 407px 199.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 150.092px 7.75px; transform-origin: 150.092px 7.75px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSatellite and Space Engineering - Problem #8\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 360.592px 7.75px; transform-origin: 360.592px 7.75px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eThis is part of a series of problems looking at topics in satellite and space communications and systems engineering.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 382.633px 7.75px; transform-origin: 382.633px 7.75px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003elf you have competed the previous exercises in this series, you will have more-or-less everything that you need to complete this problem.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 381.592px 7.75px; transform-origin: 381.592px 7.75px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eKnowing the parameters of a radio transmitter and receiver, determine the wanted signal power (dBW) in the radio receiver (in this case we are thinking of a satellite receiver, but the approach is generic to all radio receivers).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 380.425px 7.75px; transform-origin: 380.425px 7.75px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou are given power (dBW) of the signal applied to the transmitting dish antenna, the diameters (m) and efficiencies (%) of the transmitting and receiving dishes, the path length (km) between the transmitting and receiving antennas, and the frequency of the transmitted signal (GHz). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.7833px 7.75px; transform-origin: 28.7833px 7.75px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint: See\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.75px; transform-origin: 1.94167px 7.75px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Link_budget#Equation\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ehttps://en.wikipedia.org/wiki/Link_budget#Equation\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 186.308px 7.75px; transform-origin: 186.308px 7.75px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e - For this simplified exercise, you should ignore transmitter, receiver and miscelaneous losses.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 7.75px; transform-origin: 384px 7.75px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample: For a Ka-Band GSO space-to-Earth link at 17.7 GHz and of path length 41,130.13 km, where the satellite antenna has an input RF power of 9.5 dBW, a diameter of 75cm and an efficiency of 70%, and the signal is received on an Earth-station antenna of diameter 65cm and efficiency 65%, the RF power in the satellite receiver is around -119.1 dBW.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 380.433px 7.75px; transform-origin: 380.433px 7.75px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eSome future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function p = link_budget(txpower, txdiam, rxdiam, txeff, rxeff, pathlength, freq)\r\n  p = txpower+txdiam+rxdiam+txeff+rxeff+pathlength+freq;\r\nend","test_suite":"%% GSO Case from example\r\ntxpower=9.5;\r\ntxdiam=0.75;\r\nrxdiam=0.65;\r\ntxeff=70;\r\nrxeff=65;\r\npathlength=41130.13;\r\nfreq=17.7;\r\nrxpower=link_budget(txpower, txdiam, rxdiam, txeff, rxeff, pathlength, freq);\r\ny_correct = -119.1187;\r\nassert(abs(rxpower-y_correct)\u003c0.0001)\r\n\r\n%% S-Band NGSO\r\ntxpower=0.5;\r\ntxdiam=0.15;\r\nrxdiam=0.45;\r\ntxeff=70;\r\nrxeff=60;\r\npathlength=500;\r\nfreq=1.5;\r\nrxpower=link_budget(txpower, txdiam, rxdiam, txeff, rxeff, pathlength, freq);\r\ny_correct = -128.7736;\r\nassert(abs(rxpower-y_correct)\u003c0.0001)\r\n\r\n%% W-Band MGSO\r\ntxpower=10;\r\ntxdiam=0.2;\r\nrxdiam=0.75;\r\ntxeff=75;\r\nrxeff=60;\r\npathlength=10525;\r\nfreq=76;\r\nrxpower=link_budget(txpower, txdiam, rxdiam, txeff, rxeff, pathlength, freq);\r\ny_correct = -104.4088;\r\nassert(abs(rxpower-y_correct)\u003c0.0001)\r\n\r\n%% Earth-Moon Link at L-band\r\ntxpower=12;\r\ntxdiam=1.2;\r\nrxdiam=12.4;\r\ntxeff=75;\r\nrxeff=65;\r\npathlength=384400;\r\nfreq=1.6;\r\nrxpower=link_budget(txpower, txdiam, rxdiam, txeff, rxeff, pathlength, freq);\r\ny_correct = -126.9161;\r\nassert(abs(rxpower-y_correct)\u003c0.0001)\r\n\r\n%% Block obvious cheats\r\ns=importdata('link_budget.m');\r\ny_correct=false;\r\nassert(isequal(sum(contains(s,'regexp')),y_correct),'Regexp not allowed');\r\nassert(isequal(sum(contains(s,'assert')),y_correct), 'Assert not allowed');","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":437780,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":42,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-06-09T20:07:25.000Z","updated_at":"2026-04-02T19:06:40.000Z","published_at":"2022-01-04T15:40:10.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSatellite and Space Engineering - Problem #8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eThis is part of a series of problems looking at topics in satellite and space communications and systems engineering.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003elf you have competed the previous exercises in this series, you will have more-or-less everything that you need to complete this problem.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eKnowing the parameters of a radio transmitter and receiver, determine the wanted signal power (dBW) in the radio receiver (in this case we are thinking of a satellite receiver, but the approach is generic to all radio receivers).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are given power (dBW) of the signal applied to the transmitting dish antenna, the diameters (m) and efficiencies (%) of the transmitting and receiving dishes, the path length (km) between the transmitting and receiving antennas, and the frequency of the transmitted signal (GHz). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: See\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Link_budget#Equation\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttps://en.wikipedia.org/wiki/Link_budget#Equation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e - For this simplified exercise, you should ignore transmitter, receiver and miscelaneous losses.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample: For a Ka-Band GSO space-to-Earth link at 17.7 GHz and of path length 41,130.13 km, where the satellite antenna has an input RF power of 9.5 dBW, a diameter of 75cm and an efficiency of 70%, and the signal is received on an Earth-station antenna of diameter 65cm and efficiency 65%, the RF power in the satellite receiver is around -119.1 dBW.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSome future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":45809,"title":"SatCom #9: Overall Link Performance ","description":"Satellite and Space Engineering - Problem #9\r\nThis is part of a series of problems looking at topics in satellite and space communications and systems engineering.\r\nlf you have competed the previous exercises in this series, you will have more-or-less everything that you need to complete this problem.\r\nKnowing the parameters of a radio transmitter and receiver, determine the received signal 'quality' expresed as a carrier-to-noise ratio (in dB) in the radio receiver (in this case we are thinking of a satellite receiver, but the approach is generic to all radio receivers).\r\nYou are given power (dBW) of the signal applied to the transmitting dish antenna, the diameters (m) and efficiencies (%) of the transmitting and receiving dishes, the path length (km) between the transmitting and receiving antennas, and the frequency of the transmitted signal (GHz). You are also given the receiver noise tempterature (K) and bandwidth (MHz).\r\nHint: The carrier-to-noise ratio is the ratio between the received signal power in the radio receiver (see Problem #8) and the thermal noise in the receiver (see Problem #7). Typically it will be expressed in dB terms.\r\nExample: For a Ka-Band GSO space-to-Earth link at 17.7 GHz and of path length 41,130.13 km, where the satellite antenna has an input RF power of 9.5 dBW, a diameter of 75cm and an efficiency of 70%, and the signal is received on an Earth-station antenna of diameter 65cm and efficiency 65%, and where the receiver has a bandwidth of 10 MHz and a noise temperature of 220 K, the carrier-to-noise ratio in the satellite receiver is around 6.1 dB.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 390px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 195px; transform-origin: 407px 195px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 150.092px 7.75px; transform-origin: 150.092px 7.75px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSatellite and Space Engineering - Problem #9\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 360.592px 7.75px; transform-origin: 360.592px 7.75px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eThis is part of a series of problems looking at topics in satellite and space communications and systems engineering.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 382.633px 7.75px; transform-origin: 382.633px 7.75px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003elf you have competed the previous exercises in this series, you will have more-or-less everything that you need to complete this problem.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 380.375px 7.75px; transform-origin: 380.375px 7.75px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eKnowing the parameters of a radio transmitter and receiver, determine the received signal 'quality' expresed as a carrier-to-noise ratio (in dB) in the radio receiver (in this case we are thinking of a satellite receiver, but the approach is generic to all radio receivers).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 380.425px 7.75px; transform-origin: 380.425px 7.75px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou are given power (dBW) of the signal applied to the transmitting dish antenna, the diameters (m) and efficiencies (%) of the transmitting and receiving dishes, the path length (km) between the transmitting and receiving antennas, and the frequency of the transmitted signal (GHz). You are also given the receiver noise tempterature (K) and bandwidth (MHz).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.158px 7.75px; transform-origin: 383.158px 7.75px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint: The carrier-to-noise ratio is the ratio between the received signal power in the radio receiver (see Problem #8) and the thermal noise in the receiver (see Problem #7). Typically it will be expressed in dB terms.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 7.75px; transform-origin: 384px 7.75px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample: For a Ka-Band GSO space-to-Earth link at 17.7 GHz and of path length 41,130.13 km, where the satellite antenna has an input RF power of 9.5 dBW, a diameter of 75cm and an efficiency of 70%, and the signal is received on an Earth-station antenna of diameter 65cm and efficiency 65%, and where the receiver has a bandwidth of 10 MHz and a noise temperature of 220 K, the carrier-to-noise ratio in the satellite receiver is around 6.1 dB.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function cton = link_performance(txpower, txdiam, rxdiam, txeff, rxeff, pathlength, freq, rxbandwidth, rxtemp)\r\n  cton = txpower+txdiam+rxdiam+txeff+rxeff+pathlength+freq+rxbandwidth+rxtemp;\r\nend","test_suite":"%% GSO Case from example\r\ntxpower=9.5;\r\ntxdiam=0.75;\r\nrxdiam=0.65;\r\ntxeff=70;\r\nrxeff=65;\r\npathlength=41130.13;\r\nfreq=17.7;\r\nrxbandwidth=10;\r\nrxtemp=220;\r\ncton=link_performance(txpower, txdiam, rxdiam, txeff, rxeff, pathlength, freq, rxbandwidth, rxtemp);\r\ny_correct = 6.0562;\r\nassert(abs(cton-y_correct)\u003c0.0001)\r\n\r\n%% S-Band NGSO\r\ntxpower=0.5;\r\ntxdiam=0.15;\r\nrxdiam=0.45;\r\ntxeff=70;\r\nrxeff=60;\r\npathlength=500;\r\nfreq=1.5;\r\nrxbandwidth=0.05;\r\nrxtemp=180;\r\ncton=link_performance(txpower, txdiam, rxdiam, txeff, rxeff, pathlength, freq, rxbandwidth, rxtemp);\r\ny_correct = 20.2831;\r\nassert(abs(cton-y_correct)\u003c0.0001)\r\n\r\n%% W-Band MEO\r\ntxpower=10;\r\ntxdiam=0.2;\r\nrxdiam=0.75;\r\ntxeff=75;\r\nrxeff=60;\r\npathlength=10525;\r\nfreq=76;\r\nrxbandwidth=50;\r\nrxtemp=315;\r\ncton=link_performance(txpower, txdiam, rxdiam, txeff, rxeff, pathlength, freq, rxbandwidth, rxtemp);\r\ny_correct = 12.2175;\r\nassert(abs(cton-y_correct)\u003c0.0001)\r\n\r\n%% Earth-Moon Link at L-band\r\ntxpower=12;\r\ntxdiam=1.2;\r\nrxdiam=12.4;\r\ntxeff=75;\r\nrxeff=65;\r\npathlength=384400;\r\nfreq=1.6;\r\nrxbandwidth=20;\r\nrxtemp=125;\r\ncton=link_performance(txpower, txdiam, rxdiam, txeff, rxeff, pathlength, freq, rxbandwidth, rxtemp);\r\ny_correct = -2.2963;\r\nassert(abs(cton-y_correct)\u003c0.0001)\r\n\r\n%% Block obvious cheats\r\ns=importdata('link_performance.m');\r\ny_correct=false;\r\nassert(isequal(sum(contains(s,'regexp')),y_correct),'Regexp not allowed');\r\nassert(isequal(sum(contains(s,'assert')),y_correct), 'Assert not allowed');","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":437780,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":33,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-06-09T20:08:17.000Z","updated_at":"2026-04-02T19:23:51.000Z","published_at":"2022-01-04T17:03:30.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSatellite and Space Engineering - Problem #9\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eThis is part of a series of problems looking at topics in satellite and space communications and systems engineering.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003elf you have competed the previous exercises in this series, you will have more-or-less everything that you need to complete this problem.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eKnowing the parameters of a radio transmitter and receiver, determine the received signal 'quality' expresed as a carrier-to-noise ratio (in dB) in the radio receiver (in this case we are thinking of a satellite receiver, but the approach is generic to all radio receivers).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are given power (dBW) of the signal applied to the transmitting dish antenna, the diameters (m) and efficiencies (%) of the transmitting and receiving dishes, the path length (km) between the transmitting and receiving antennas, and the frequency of the transmitted signal (GHz). You are also given the receiver noise tempterature (K) and bandwidth (MHz).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: The carrier-to-noise ratio is the ratio between the received signal power in the radio receiver (see Problem #8) and the thermal noise in the receiver (see Problem #7). Typically it will be expressed in dB terms.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample: For a Ka-Band GSO space-to-Earth link at 17.7 GHz and of path length 41,130.13 km, where the satellite antenna has an input RF power of 9.5 dBW, a diameter of 75cm and an efficiency of 70%, and the signal is received on an Earth-station antenna of diameter 65cm and efficiency 65%, and where the receiver has a bandwidth of 10 MHz and a noise temperature of 220 K, the carrier-to-noise ratio in the satellite receiver is around 6.1 dB.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":45812,"title":"SatCom #10: Rate of Precesion of Orbit Plane (Nodal Precession)","description":"Satellite and Space Engineering - Problem #10\r\nThis is part of a series of problems looking at topics in satellite and space communications and systems engineering.\r\nProblem #5 has already looked at the  'Sun-Synchronous Orbit' which has the special feature that the plane of the orbit precesses (rotates) in inertial space at exactly the same rate as the earth rotates around the sun. Therefore, the orbit plane always maintains a fixed angle with respect to the sun, which means that the satellite always passes over the same point on the ground at the same local mean solar time. \r\nA more general way of looking at what is going on for this type of orbit is to note that the rate of precession changes depending on the way that the orbit is configured. The unequal forces on the satellite caused by the equatorial bulge of the Earth tends will make an inclined orbit precess at a different angular rate depending on the orbit configuration. This precession is often called the 'nodal precession' of the orbit, because the points at which the orbit crosses the equator (the 'nodes') precess around the Earth as the orbit precesses.\r\nYou are given the satellite orbit's apogee and perigee altitudes (in km) and the inclination (in degrees). You should calculate the nodal precession rate (in degrees per day) for that orbit.\r\nHint : See https://formulasearchengine.com/wiki/Nodal_precession for a detailed explanation of how to derive the nodal precession rate of a satellite orbit.\r\nYou should take the radius of the Earth to be 6378137 m,  the second zonal gravity harmonic of the Earth (J2 term) as 0.0010826269, and the Earth standard gravitational parameter as  3.986004418e14 (m^3/s^2).\r\nExample: The CLOUDSAT satellite has an apogee of 710 km and a perigee of 709 km. It's orbit inclination is approximately 98.2 degrees. Its nodal precession rate is approximately 0.9825.\r\nSome future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 513px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 256.5px; transform-origin: 407px 256.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 153.983px 7.75px; transform-origin: 153.983px 7.75px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSatellite and Space Engineering - Problem #10\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 360.592px 7.75px; transform-origin: 360.592px 7.75px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eThis is part of a series of problems looking at topics in satellite and space communications and systems engineering.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 368.692px 7.75px; transform-origin: 368.692px 7.75px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eProblem #5 has already looked at the  'Sun-Synchronous Orbit' which has the special feature that the plane of the orbit precesses (rotates) in inertial space at exactly the same rate as the earth rotates around the sun. Therefore, the orbit plane always maintains a fixed angle with respect to the sun, which means that the satellite always passes over the same point on the ground at the same local mean solar time. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 105px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 52.5px; text-align: left; transform-origin: 384px 52.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 359.392px 7.75px; transform-origin: 359.392px 7.75px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA more general way of looking at what is going on for this type of orbit is to note that the rate of precession changes depending on the way that the orbit is configured. The unequal forces on the satellite caused by the equatorial bulge of the Earth tends will make an inclined orbit precess at a different angular rate depending on the orbit configuration. This precession is often called the 'nodal precession' of the orbit, because the points at which the orbit crosses the equator (the 'nodes') precess around the Earth as the orbit precesses.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.233px 7.75px; transform-origin: 383.233px 7.75px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou are given the satellite orbit's apogee and perigee altitudes (in km) and the inclination (in degrees). You should calculate the nodal precession rate (in degrees per day) for that orbit.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32.6667px 7.75px; transform-origin: 32.6667px 7.75px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint : See \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://formulasearchengine.com/wiki/Nodal_precession\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ehttps://formulasearchengine.com/wiki/Nodal_precession\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 164.158px 7.75px; transform-origin: 164.158px 7.75px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for a detailed explanation of how to derive the nodal precession rate of a satellite orbit.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 366.133px 7.75px; transform-origin: 366.133px 7.75px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou should take the radius of the Earth to be 6378137 m,  the second zonal gravity harmonic of the Earth (J2 term) as 0.0010826269, and the Earth standard gravitational parameter as  3.986004418e14 (m^3/s^2).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 382.4px 7.75px; transform-origin: 382.4px 7.75px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample: The CLOUDSAT satellite has an apogee of 710 km and a perigee of 709 km. It's orbit inclination is approximately 98.2 degrees. Its nodal precession rate is approximately 0.9825.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 380.433px 7.75px; transform-origin: 380.433px 7.75px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eSome future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function prate = nodal_precession(apogee, perigee, inclination)\r\n   prate = apogee+perigee+inclination;\r\nend","test_suite":"%%\r\napogee = 710;\r\nperigee = 709;\r\ninclination = 98.2;\r\ny_correct = 0.9825;\r\nprate = nodal_precession(apogee, perigee, inclination);\r\nassert(abs(prate-y_correct)\u003c0.0001)\r\n\r\n%%\r\napogee = 282;\r\nperigee = 282;\r\ninclination = 45;\r\ny_correct = -6.0556;\r\nprate = nodal_precession(apogee, perigee, inclination);\r\nassert(abs(prate-y_correct)\u003c0.0001)\r\n\r\n%%\r\napogee = 5172;\r\nperigee = 5172;\r\ninclination = 90;\r\ny_correct = 0;\r\nprate = nodal_precession(apogee, perigee, inclination);\r\nassert(abs(prate-y_correct)\u003c0.0001)\r\n\r\n%%\r\napogee = 9344;\r\nperigee = 1000;\r\ninclination = 63.5;\r\ny_correct = -0.7358;\r\nprate = nodal_precession(apogee, perigee, inclination);\r\nassert(abs(prate-y_correct)\u003c0.0001)\r\n\r\n%%\r\ns=importdata('nodal_precession.m');\r\ny_correct=false;\r\nassert(isequal(sum(contains(s,'regexp')),y_correct),'Regexp not allowed');\r\nassert(isequal(sum(contains(s,'assert')),y_correct),'Assert not allowed');","published":true,"deleted":false,"likes_count":3,"comments_count":5,"created_by":437780,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":37,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-06-09T20:09:29.000Z","updated_at":"2026-04-03T15:22:19.000Z","published_at":"2022-01-04T17:41:03.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSatellite and Space Engineering - Problem #10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eThis is part of a series of problems looking at topics in satellite and space communications and systems engineering.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eProblem #5 has already looked at the  'Sun-Synchronous Orbit' which has the special feature that the plane of the orbit precesses (rotates) in inertial space at exactly the same rate as the earth rotates around the sun. Therefore, the orbit plane always maintains a fixed angle with respect to the sun, which means that the satellite always passes over the same point on the ground at the same local mean solar time. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA more general way of looking at what is going on for this type of orbit is to note that the rate of precession changes depending on the way that the orbit is configured. The unequal forces on the satellite caused by the equatorial bulge of the Earth tends will make an inclined orbit precess at a different angular rate depending on the orbit configuration. This precession is often called the 'nodal precession' of the orbit, because the points at which the orbit crosses the equator (the 'nodes') precess around the Earth as the orbit precesses.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are given the satellite orbit's apogee and perigee altitudes (in km) and the inclination (in degrees). You should calculate the nodal precession rate (in degrees per day) for that orbit.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint : See \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://formulasearchengine.com/wiki/Nodal_precession\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttps://formulasearchengine.com/wiki/Nodal_precession\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for a detailed explanation of how to derive the nodal precession rate of a satellite orbit.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou should take the radius of the Earth to be 6378137 m,  the second zonal gravity harmonic of the Earth (J2 term) as 0.0010826269, and the Earth standard gravitational parameter as  3.986004418e14 (m^3/s^2).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample: The CLOUDSAT satellite has an apogee of 710 km and a perigee of 709 km. It's orbit inclination is approximately 98.2 degrees. Its nodal precession rate is approximately 0.9825.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSome future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"no_progress_badge":{"id":53,"name":"Unknown","symbol":"unknown","description":"Partially completed groups","description_html":null,"image_location":"/images/responsive/supporting/matlabcentral/cody/badges/problem_groups_unknown_2.png","bonus":null,"players_count":0,"active":false,"created_by":null,"updated_by":null,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"created_at":"2018-01-10T23:20:29.000Z","updated_at":"2018-01-10T23:20:29.000Z","community_badge_id":null,"award_multiples":false}}